# 1 = 0.999

1 = 0.99999

Algebraic proof -

Let's say x = 0.999999(infinitely)

10 = 10x

10 - 1 = 10x - x =9.9999(infinitely) - 0.99999(infinitely) = 9

9 = 9

We haven't reached a Reductio Ad Absurdum so our assumption must have been true, which means that

$\boxed{1 = 0.99(Infinitely)}$ Note by A Former Brilliant Member
4 months, 1 week ago

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Hahaha! Check out this problem :-)

- 4 months, 1 week ago

Vinayak used the same Logic. :)

- 4 months, 1 week ago

- 4 months, 1 week ago

Nice, I never thought of the infinite series like that. Awesome!!

- 4 months, 1 week ago

I upvoted!! :-)

- 4 months, 1 week ago

Thank you!

- 4 months, 1 week ago

First, i didn't understand why you took 1.8, then I understood, - 1.8 + 0.18 = 1.99. Nice!! Your solution is the best!!

- 4 months, 1 week ago

I put a shimmering heart emoji on it as a comment.

- 4 months, 1 week ago

This is not a right way to prove, there is a way called proof by contradiction, but if from an assumption. If you haven't reached to a contradiction yet this doesn't mean that the assumption was correct. Maybe a contradiction may come out after sometime.

- 4 months, 1 week ago

My solution is bad or the Former Brilliant Member's solution is bad?

- 4 months, 1 week ago

Former Brilliant Member's solution is bad, because he wanted to explain this

Let $\text{x = 0.999.....}$

$\text{10x = 9.999.....}$

$\text{10x = 9 + 0.999.....}$

$\text{10x = 9 + x}$

$\text{9x = 9}$

$\text{x = 1}$

$\text{1 = 0.999.....}$

but did it in the wrong way

- 4 months, 1 week ago